Averages (including IQR): WJEC GCSE Numeracy Foundation November 2024 Unit 2 Q3

Numeracy Foundation November 2024 Unit 2 Q3

3. Dafydd plays football for his local team.

(a)

Dafydd is working on his fitness.
Dafydd uses this formula to calculate his Body Mass Index (BMI):

BMI = mass ÷ height²

where mass is in kilograms and height is in metres

Football players should have a BMI between 18 and 24·9.

Dafydd’s mass is 79 kg and his height is 1·8 m.

Calculate Dafydd’s BMI. [2]

(b)

Dafydd’s first game of football was on Saturday.
The match started at 3 p.m.

The playing time of the match was \(1\frac{1}{2}\) hours.
Half time was 15 minutes long.
After the game, the players completed cool-down exercises and stretching for 20 minutes.
Dafydd took 25 minutes to shower and change.
The journey home took 45 minutes.

At what time did Dafydd arrive home?
You must show all your working. [3]

(c)

The list below shows the number of goals that Dafydd’s football team scored in each of their last 7 games.

3 1 6 3 1 1 2

The football coach looks at this data.

(i)

The coach says,

“The median number of goals scored per game is three.”

Show that the coach is not correct. [2]

(ii) What is the mode of the number of goals scored per game for the team? [1]

(iii) Calculate the range of the number of goals scored per game. [1]

Mark scheme (a)

Scheme	Marks	Comments
79 ÷ 1.8² 24(.3827…)	M1 A1	Ignore subsequent rounding if 24(.3827…. ) seen. Accept rounded or truncated answers e.g. 24.3 or 24.4 Do not accept an answer of 25 unless 24(.3827…) seen If correct answer seen with 79 ÷ 1.8 award M1A1

Mark scheme (b)

Scheme	Marks	Comments
(Time taken =) 3 hours 15 mins or 195 mins	B2	B1 any one of the following: clearly calculating 1½ hrs + 15 mins + 20 mins + 25 mins + 45 mins Allow use of 01:30 + 00:15 + 00:20 + 00:25 + 00:45 1 hour 45 mins or 105 mins (1 ½ hours omitted) 3 hours or 180 mins (15 mins omitted) 2 hours 55 mins or 175 mins (20 mins omitted) 2 hours 50 mins or 170 mins (25 mins omitted) 2 hours 30 mins or 150 mins (45 mins omitted)
(Earliest arrival home is) 6:15 (pm) or 18(:)15	B1	Award B2 B0 for 6:15 am FT ‘their 3 hours 15 mins’ or ‘their 195 mins’ provided B1 awarded

The alternative method is printed in italics in the mark scheme.

3(b) Alternative method – adding times to 3 p.m.

Scheme	Marks	Comments
(Earliest arrival home is) 6:15 (pm) or 18(:)15	B3	B2 for: an answer of 6:15 am an answer that includes correct step-by-step calculations with at most one error or omission. FT from their one error or omission B1 for an answer that includes correct step-by-step calculations with at most two errors or omissions. FT from their 2 errors or omissions 3 correctly calculated steps. FT from their 2 errors or omissions

Mark scheme (c)

Scheme	Marks	Comments
(i) (size order) 1, 1, 1, 2, 3, 3, 6 (median=) 2	M1 A1	Accept indication of median is 2 e.g. circling of 2 when numbers are in size order. Do not award M1A1 for an unsupported answer of 2. Award SC1 for an unsupported answer of 2.
(ii) 1	B1
(iii) 5	B1